Question: Rewrite as a simplified fraction. ${1.7\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 178.8888...\\ 10x &= 17.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 161}$ ${x = \dfrac{161}{90}} \text{or} {1 \dfrac{71}{90}}$